New punctures for six-dimensional compactifications

TL;DR

This work develops a holographic framework to study codimension-two punctures in four-dimensional theories arising from compactifications of six-dimensional ${\cal N}=(1,0)$ and ${\cal N}=(2,0)$ SCFTs, using probe branes in massive IIA AdS$_7$ and AdS$_5$ backgrounds. By computing defect Weyl anomalies and related observables (A-type anomaly $a$, defect $d_2$, sphere partition functions, and entanglement/Rényi entropies) for D4 and D6/D4 probes, the authors connect puncture data to gravity via explicit formulas, reproduce known class S results in the appropriate limit, and predict new ${\cal N}=1$ punctures for ${\cal N}=(1,0)$ theories, including those arising from class Sk orbifolds and beyond. They show that puncture contributions factorize in large-$N$ limits and provide concrete holographic predictions for anomaly coefficients of novel punctures, thereby offering a bridge between gravity solutions and 4d SCFT data. The results yield a quantitative framework to test and extend the classification of 4d SCFTs obtained from 6d compactifications, with specific predictions for defect central charges and their scaling with flux quanta and quiver data.

Abstract

Six-dimensional superconformal field theories (SCFTs) give rise to four-dimensional (4d) ones when compactified on Riemann surfaces. In the $\mathcal{N}=(2,0)$ case, this yields the famous class S family. For $\mathcal{N}=(1,0)$ theories that arise from linear unitary quivers, the holographic duals of the 4d theories are known in massive IIA supergravity, but only without punctures. Working in the probe approximation, we identify all possible BPS punctures in these models and characterize them by computing their defect Weyl anomalies. For class S, our results reproduce the known expressions in the appropriate limit. In the more general $\mathcal{N}=(1,0)$ case, they predict new 4d SCFTs and their large-$N$ anomaly coefficients.

Figures (1)

• Figure 1: Left: The interval $[z_-,z_+]$ is defined as the region where $\alpha>\alpha_0$. The D6/D4 consists of a meridian of $\mathds{S}^2$ at $\cos\theta=\alpha_0/\alpha$, which degenerates to a point at $z=z_\pm$. Right: A two-dimensional cartoon of the internal space $M_3$ and of some brane probes. The $\mathds{S}^2$ is represented as a circle parameterized by $\theta$, suppressing the $\varphi$ direction. We show two examples of D6/D4 branes, and a single D4, which can be thought of as the limit $\alpha_0=\alpha_\mathrm{max}$. A general puncture is obtained by placing several of these objects over the same point in $\Sigma$.